Weakly coupled dynamical systems and applications

Abstract

In this article, we define a new class of dynamical systems that are not associated with semigroups and that we call weakly coupled systems (in the sense that the initial conditions for the different components of the system are not independent) and study the asymptotic behavior of such systems. In particular, we define and study the notions of global attractor, inertial manifold and exponential attractor associated with a weakly coupled system. We also consider the nonautonomous case. As an example, we study the asymptotic behavior of weakly coupled Cahn–Hilliard equations.